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We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier-Stokes equations. We control the thickness of the film at the take-up point using the shape of the nozzle. The control goal consists in finding an even thickness profile. To achieve this goal, we minimize an appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method. The gradient of the cost functional is approximated using the adjoint variables of the problem with fixed film width. Numerical simulations show the applicability of the proposed method.

An optimal control problem for a mathematical model of a melt spinning process is considered. Newtonian and non--Newtonian models are used to describe the rheology of the polymeric material, the fiber is made of. The extrusion velocity of the polymer at the spinneret as well as the velocity and temperature of the quench air serve as control variables. A constrained optimization problem is derived and the first--order optimality system is set up to obtain the adjoint equations. Numerical solutions are carried out using a steepest descent algorithm.